Given a normal distribution with mu equals 100=100 and sigma equals 10 comma=10,

Question

Given a normal distribution with

mu equals 100=100

and

sigma equals 10 comma=10,

complete parts (a) through (d).

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a. What is the probability that

Upper X greater than 85X>85?

The probability that

Upper X greater than 85X>85

is

0.93320.9332.

(Round to four decimal places as needed.)

b. What is the probability that

Upper X less than 75X<75?

The probability that

Upper X less than 75X<75

is

0.00620.0062.

(Round to four decimal places as needed.)

c. What is the probability that

Upper X less than 95X<95

or

Upper X greater than 125X>125?

The probability that

Upper X less than 95X<95

or

Upper X greater than 125X>125

is

0.31470.3147.

(Round to four decimal places as needed.)

d.

9090%

of the values are between what two X-values (symmetrically distributed around the mean)?

9090%

of the values are greater than

nothing

and less than

nothing.

(Round to two decimal places as needed.)

Explanation / Answer

d) P(-x < X < x) = 0.9

or, P(-z < Z < z) = 0.9

or, P(Z < z) - P(Z < -z) = 0.9

or, P(Z < z) - (1 - P(Z < z)) = 0.9

or, 2P(Z < z) = 1.9

or, P(Z < z) = 0.95

or, z = 1.645

or, (x - 100)/10 = 1.645

or, x = 1.645 * 10 + 100

or, x = 116.45

116.45 - 100 = 16.45

100 - 16.45 = 83.55

So the two values are (83.55, 116.45)

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